I had time to dig deeper.
Replicating the problem
Start with a default-sized figure. Create a stacked plot and an annotation rectangle placed at x=[1,3]. Note that I'm using the stackedplot position to compute the annotation rectangle position. Don't use undocumented methods to access the axes here.
fig = figure('Position', get(groot,'factoryFigurePosition'));
data = rand(10,5).*[ones(3,1);8*ones(7,1)];
hEdgeNorm = dh.Position(1) + (hEdgeData-min(xlim(dh)))/range(xlim(dh))*dh.Position(3);
hWidth = diff(hEdgeNorm);
ah = annotation('rectangle',[hEdgeNorm(1),dh.Position(2),hWidth,dh.Position(4)],...
'Color', 'r', 'LineWidth', 2, 'LineStyle', '--');
After the stackedplot is rendered, change the figure size to half the width and height
fig.Position(3:4) = fig.Position(3:4)./2;
Explanation of the problem
The annotation rectangle is in normalized figure units. When the stackedplot size decreases, its position changes so the annotation rectangle is no longer in the intended position over the stackedplot.
Solution 1: Position constraint
An easy solution is to set the stackedplot's PositionConstraint to innerposition but this comes with a caveat. When the PositionConstrain is set to innerposition, the y axis labels may extend beyond the figure frame when the figure size is reduced.
dh.PositionConstraint = 'innerposition';
This is the result of the problem set above.
Solution 2: Add a listener that updates annotation rectangle upon position change
Whenever the stackedplot OuterPosition is changed, the listener will update the annotation rectangle. Set the figure to the desired size before exporting.
See inline comments for further explanation.
data = rand(10,5).*[ones(3,1);8*ones(7,1)];
stackHandle = stackedplot(data);
annotHandle = annotation('rectangle',zeros(1,4),...
'Color', 'r', 'LineWidth', 2, 'LineStyle', '--');
fig.UserData.PositionListener = addlistener(stackHandle,'OuterPositionChanged',@(h,evt)updateAnnotationPosition(h,evt,annotHandle));
updateAnnotationPosition(stackHandle,[],annotHandle)
function updateAnnotationPosition(stackHandle,~,annotationHandle)
hEdgeNorm = stackHandle.Position(1) + (hEdgeData-min(xlim(stackHandle)))/range(xlim(stackHandle))*stackHandle.Position(3);
hWidth = diff(hEdgeNorm);
annotationHandle.Position = [hEdgeNorm(1),stackHandle.Position(2),hWidth,stackHandle.Position(4)];
Final result:
